Curvature-based Feature Representation for Ship Detection in SAR Image

This article aims to exploit Ricci tensor with certain geometric properties which are used for feature representation and ship detection in synthetic aperture radar (SAR) image. The proposed method is composed of the following key points. Firstly, Riemannian metrics on the Gamma manifold are constructed based on the family of Gamma density functions. Secondly, direct calculation gives the Ricci tensor of Gamma manifold, where the curvature tensor resorts to the torsion-free affine connection. Thirdly, a general scheme for Zermelo navigation problem on the Riemannian manifold is addressed, and the solution of the navigation problem is proposed. Fourthly, feature representation problems are formulated as certain forms of Finsler metric of Randers type, indicating a joint framework for extracting low-dimensional features with closed-form solutions. Comprehensive experiments on real SAR image data sets demonstrate the effectiveness of the proposed method against compared state-of-the-art detection approaches.